ASSET PRICING WITH NO EXOGENOUS PROBABILITY MEASURE

Authors


  • I owe my gratitude to Robert J. Elliot and William Sudderth for their kind encouragement, and to M. Rasony and two anonymous referees for a number of useful suggestions. The usual disclaimer applies.

Address correspondence to Gianluca Cassese, Istituto di Economica Politica, Universita Commerciale L. Bocconi, via U. Gobi, 5-120136 Milano,Italy; e-mail: gianluca.cassese@uni.bocconi.it.

Abstract

In this paper, we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on finitely additive measures. From this representation we derive an exact decomposition of the risk premium as the sum of the correlation of returns with the market price of risk and an additional term, the purely finitely additive premium, related to the jumps of the return process. We also discuss the implications of the absence of free lunches.

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